Mecha Godzilla:
Press L, R, Y, X, A, B at the title screen.

Spacecraft:
Hold L + R and press Up, Left, Right, Down, Y, X, B, A at the title screen.

Hint: Start with Super Fireball:
Hold Y when powering on the game. When you start, you will get the Super Fireball. Note: This does not work for certain game paks.